There are many different ways we can classify numbers. In fact,
many of the classifications are subsets of other classifications. For example, the set of counting/natural numbers differ from the set of whole numbers by excluding 0. Therefore, the set of counting/natural numbers is a subset of the set of whole numbers. The following table
gives depictions of how the classifications relate:

Counting/Natural Numbers 
Whole Numbers 
Integers 
Rationals 
Irrationals 
Examples 
1, 2, 3, 4,... 
0, 1, 2, 3, 4,... 
…, 3, 2, 1, 0, 1, 2, 3, ... 
1/4, 6/5, 0.125, 3.272727 
, 2.345678... 
What's new 

0 
Opposites of natural numbers 
Fractions, repeating and terminating
decimals 
nonterminating, nonrepeating
decimals 
Together the rational and irrational numbers form a larger set of
numbers called the Real Numbers.
